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 11 does not divide any of them (Posted on 2012-12-26)
How many palindromes below 10000 (i.e. between 0 and 9999 inclusively) are not divisible by 11?
List them.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 Just counting (spoiler) | Comment 1 of 3
A number is divisible by 11 if and only if the sum of its odd-numbered digits (1st digit, 3rd digit, 5th digit, etc.) minus the sum of its odd-numbered digits are divisible by 11.  Thus, all palindromes with an even number of digits are divisible by 11.  Thus, we must only consider palindromes with an odd number of digits.

All 10 one-digit numbers ( 0, 1, ... 8, 9) qualify.
Also, all 90 of the 3 digit palindromes except:
121
242
363
484
616
737
858
979

In other words, 10 + 90 - 8 = 92.  Too many for me to list.

 Posted by Steve Herman on 2012-12-26 17:20:54

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